TY - JOUR
T1 - On the conjugacy relation in ergodic theory
AU - Foreman, Matthew D.
AU - Rudolph, Daniel J.
AU - Weiss, Benjamin
PY - 2006/11/15
Y1 - 2006/11/15
N2 - The set of pairs of transformations on the interval [0, 1] can be equipped with a standard Borel structure. We prove that the relation of conjugacy is not a Borel subset of this space, in fact it is complete analytic. Moreover, our construction proves that the two sets, {T : T is conjugate of T-1}, and {T : the centralizer of T is non-trivial} are complete analytic sets. To cite this article: M.D. Foreman et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).
AB - The set of pairs of transformations on the interval [0, 1] can be equipped with a standard Borel structure. We prove that the relation of conjugacy is not a Borel subset of this space, in fact it is complete analytic. Moreover, our construction proves that the two sets, {T : T is conjugate of T-1}, and {T : the centralizer of T is non-trivial} are complete analytic sets. To cite this article: M.D. Foreman et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).
UR - http://www.scopus.com/inward/record.url?scp=33751072066&partnerID=8YFLogxK
U2 - 10.1016/j.crma.2006.09.011
DO - 10.1016/j.crma.2006.09.011
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AN - SCOPUS:33751072066
SN - 1631-073X
VL - 343
SP - 653
EP - 656
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 10
ER -